A Microscale Percolation Model for Nanocomposite Complex Impedance

Nanofiller-modified materials have received enormous attention from the structural health monitoring (SHM) research community because they are self-sensing via the piezoresistive effect. To date, considerable effort has been dedicated to understanding the fundamental mechanisms of nanocomposite conductivity and piezoresistivity via microscale percolation models. However, nanocomposites also possess complex, frequency-dependent electrical properties. This has received much less attention with prevailing approaches only modeling the net input-output response at the macroscale as an equivalent resistor-capacitor (and sometimes inductor) or RC(L) circuit. To truly understand the underlying mechanisms of complex impedance in nanocomposites, more sophisticated models capable of accounting for nanofiller-to-nanofiller interactions are needed. To address this, a microscale percolation model for complex impedance is herein developed by introducing capacitive coupling at nanofiller-to-nanofiller junctions. This model is then calibrated against experimental data for carbon nanofiber (CNF)-modified epoxy resulting in very accurate model-to-experiment correspondence. An important insight from this work is that experimental data can only be fit by allowing for capacitive coupling beyond the electron tunneling cutoff distance typically associated with piezoresistive nanocomposites.